I'm very sorry to hear you had so much trouble at the IB counter at LAX and almost missed your flight. If I'm reading your post correctly, the problem was that you purchased a ticket for yourself and your wife more than 8 months ago, and afterwards had a baby which required a new ticket. It's too late now of course, but for my understanding, would it have been possible for you to have amended your ticket or purchased one for your infant by phone during the 8 months before flying? Either way, the LAX staff should of course been able tp help, or at least cared that you not miss your flight.
Separately, you experienced poor service in flight. I've yet to fly IB long-haul, so I have no idea how common this is. Obviously, I hope this is not typical.